A parametrization of all stabilizing controllers for linear minimum phase single-input and single-output systems

An exact parametrization is given for the class of all proper stabilizing controllers for linear minimum phase systems. This parametrization is simple and does not contain improper controllers, that is, this parametrization contains only proper stabilizing controllers. This parametrization is given by using a supplemental rational function to hold a certain condition and free-parameter. It is shown that this parametrization is independent of selection of supplemental rational functions. A control structure of all stabilizing controllers for the minimum phase system is given. A numerical example to show the effectiveness is given.